Question

Final grades for all of the sections of the data analysis class (WCOB 1033) for the spring semester are normally distributed with a mean (µ) of 75 and a standard deviation (σ) of 13. What is the approximate cutoff value for the top 5% of all the grades?

Group of answer choices

a. 86

b. 80

c. 90

d. 96

Answer 1

Given that,

mean = = 75

standard deviation = =13

Using standard normal table,

P(Z > z) =5 %

= 1 - P(Z < z) = 0.05

= P(Z < z ) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.64 ) = 0.95

z =1.64 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x=1.64 *13+75

x= 96